Battery and lag issues on DroidSupport

Ok, I have check the forums and found numerous posts about battery issues as well as lag issues. I am having both at the same time.

First off with the lag. It happens on everything, contact list, app menu, web browsing, typing messages, you name it, it lags. I have tried task killers as well as anti-virus software and nothing has helped. Tried power cycling, tried pulling the battery, even formatting the SD card. Nothing fixes this.

The lag started just about the same time as:

Battery issue. The same day the lag issue began I noticed my battery lasted about 6 hours and the phone shut off. I plugged it in, allowed it to charge to 100%. After about 30 minutes the battery was down to about 70%. Under settings -> about phone -> battery use I consistently have:

Both issues happened randomly. It was not after I changed a setting or downloaded a program. I have actually only downloaded maybe a handful of apps. Someone please let me know what is wrong and how to fix it.

Can the ota update have anything to do with battery life, been seeing alot of battery issues on many forums blaming the last update. I wouldnt know because I got the phone this past weekend and have had horrible battery life the whole time, actually thinking about taking phone back.